Prime Number Checker - Is It Prime? Factorization, Next Prime & Prime List
Prime Number Checker
Test any number for primality, factor it, and list primes in a range
Fast for Huge Numbers
Uses the Miller-Rabin test, which is exact for numbers below 3.3 × 10²⁴ and answers instantly even for 30-digit inputs.
Full Factorization
Breaks composites into prime factors with trial division and Pollard's rho, then reports divisor count and sum.
Prime Lists
List every prime between two numbers, up to 10¹², using a segmented sieve, and see how many there are.
Full Privacy
Everything is calculated in your browser.
What Is a Prime Number?
A prime is a whole number greater than 1 whose only divisors are 1 and itself: 2, 3, 5, 7, 11, 13… Every other whole number above 1 is composite and can be written in exactly one way as a product of primes, which is why primes are called the atoms of arithmetic. The number 1 is neither prime nor composite, and 2 is the only even prime.
For numbers above about 3.3 × 10²⁴ the test is probabilistic, so the page says probably prime; the chance of a wrong answer is astronomically small but not zero. Factorization of a very large number with only huge prime factors can be beyond a browser, in which case the result is marked as partly factored.
Key Takeaways
- Accurate: Deterministic and exact up to 3.3 × 10²⁴, cross-checked against a sieve in the test suite.
- Honest: Says "probably prime" or "partly factored" when it cannot be certain.
- Useful extras: Divisor count and sum, plus the neighbouring primes.